Buckling Analysis of a Functionally Graded unidirectional rectangular nanoPlate considering the surface effect

Khorshidi, Korosh; Ghasemi, Mohsen; Bahrami, Mahdi

doi:10.61186/masm.3.1.21

Buckling Analysis of a Functionally Graded unidirectional rectangular nanoPlate considering the surface effect

Document Type : Original Article

Authors

Korosh Khorshidi ¹

Mohsen Ghasemi ²

Mahdi Bahrami ³

¹ Department of mechanical engineering/Arak University/Arak/Iran

² Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran

³ Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak , Iran

https://doi.org/10.61186/masm.3.1.21

Abstract

In this paper, buckling analysis of functionally graded rectangular Nano-plates considering the surface effect is investigated. Also, to define the material properties the Mori-Tanaka scheme is used which according to this scheme the material properties change continuously along the thickness direction. Displacement field is obtained using modified shear deformation theories. In these theories, against classical plate theory, the effects of rotary inertia and transverse shear deformations are considered and various functions such as exponential, trigonometric, hyperbolic and parabolic functions are used to considering these effects along the thickness direction. To considering nonlocal and surface effects the nonlocal elasticity theory and surface elasticity theory are employed respectively. The governing equations of motion are obtained by Hamilton’s principle and the Galerkin method is used to solve these equations. To show the accuracy of the present formulations, the presented results in this thesis are compared with those reported in the literature. Finally, the effects of various parameters which is related to the surface parameters such as residual surface stress, surface elasticity constant and also other parameters such as thickness ratio, aspect ratio, material index and nonlocal parameter of functionally graded nano-plate are investigated.

Keywords

Surface effect

Buckling

Functionally graded Nano-plate

Surface elasticity theory

Nonlocal elasticity theory

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